Principles of Physics: A Calculus-Based Text
5th Edition
ISBN: 9781133104261
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 15.1, Problem 15.1QQ
Suppose you are standing directly behind someone who steps back and accidentally stomps on your foot with the heel of one shoe. Would you be better off if that person were (a) a large male professional basketball player wearing sneakers or (b) a petite woman wearing spike-heeled shoes?
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Question B3
Consider the following FLRW spacetime:
t2
ds² = -dt² +
(dx²
+ dy²+ dz²),
t2
where t is a constant.
a)
State whether this universe is spatially open, closed or flat.
[2 marks]
b) Determine the Hubble factor H(t), and represent it in a (roughly drawn) plot as a function
of time t, starting at t = 0.
[3 marks]
c) Taking galaxy A to be located at (x, y, z) = (0,0,0), determine the proper distance to galaxy
B located at (x, y, z) = (L, 0, 0). Determine the recessional velocity of galaxy B with respect
to galaxy A.
d) The Friedmann equations are
2
k
8πG
а
4πG
+
a²
(p+3p).
3
a
3
[5 marks]
Use these equations to determine the energy density p(t) and the pressure p(t) for the
FLRW spacetime specified at the top of the page.
[5 marks]
e) Given the result of question B3.d, state whether the FLRW universe in question is (i)
radiation-dominated, (ii) matter-dominated, (iii) cosmological-constant-dominated, or (iv)
none of the previous. Justify your answer.
f)
[5 marks]
A conformally…
SECTION B
Answer ONLY TWO questions in Section B
[Expect to use one single-sided A4 page for each Section-B sub question.]
Question B1
Consider the line element
where w is a constant.
ds²=-dt²+e2wt dx²,
a) Determine the components of the metric and of the inverse metric.
[2 marks]
b) Determine the Christoffel symbols. [See the Appendix of this document.]
[10 marks]
c)
Write down the geodesic equations.
[5 marks]
d) Show that e2wt it is a constant of geodesic motion.
[4 marks]
e)
Solve the geodesic equations for null geodesics.
[4 marks]
Chapter 15 Solutions
Principles of Physics: A Calculus-Based Text
Ch. 15.1 - Suppose you are standing directly behind someone...Ch. 15.2 - Prob. 15.2QQCh. 15.4 - An apple is held completely submerged just below...Ch. 15.4 - Prob. 15.4QQCh. 15.6 - Prob. 15.5QQCh. 15.7 - You observe two helium balloons floating next to...Ch. 15 - A wooden block floats in water, and a steel object...Ch. 15 - Prob. 2OQCh. 15 - Prob. 3OQCh. 15 - Prob. 4OQ
Ch. 15 - A solid iron sphere and a solid lead sphere of the...Ch. 15 - Prob. 6OQCh. 15 - Prob. 7OQCh. 15 - Prob. 8OQCh. 15 - An ideal fluid flows through a horizontal pipe...Ch. 15 - Prob. 10OQCh. 15 - Prob. 11OQCh. 15 - A small piece of steel is tied to a block of wood....Ch. 15 - A piece of unpainted porous wood barely floats in...Ch. 15 - Prob. 14OQCh. 15 - A water supply maintains a constant rate of flow...Ch. 15 - Prob. 1CQCh. 15 - Because atmospheric pressure is about 105 N/m2 and...Ch. 15 - Two thin-walled drinking glasses having equal base...Ch. 15 - Prob. 4CQCh. 15 - Prob. 5CQCh. 15 - Prob. 6CQCh. 15 - Prob. 7CQCh. 15 - Prob. 8CQCh. 15 - Prob. 9CQCh. 15 - Prob. 10CQCh. 15 - Prob. 11CQCh. 15 - Prob. 12CQCh. 15 - (a) Is the buoyant force a conservative force? (b)...Ch. 15 - An empty metal soap dish barely floats in water. A...Ch. 15 - Prob. 15CQCh. 15 - How would you determine the density of an...Ch. 15 - Prob. 17CQCh. 15 - Place two cans of soft drinks, one regular and one...Ch. 15 - Prob. 19CQCh. 15 - Prob. 1PCh. 15 - A 50.0-kg woman wearing high-heeled shoes is...Ch. 15 - Prob. 3PCh. 15 - Prob. 4PCh. 15 - Prob. 5PCh. 15 - The small piston of a hydraulic lift (Fig. P15.6)...Ch. 15 - A container is filled to a depth of 20.0 cm with...Ch. 15 - Prob. 8PCh. 15 - (a) Calculate the absolute pressure at an ocean...Ch. 15 - (a) A very powerful vacuum cleaner has a hose 2.86...Ch. 15 - What must be the contact area between a suction...Ch. 15 - Prob. 12PCh. 15 - Review. The tank in Figure P15.13 is filled with...Ch. 15 - Review. The tank in Figure P15.13 is filled with...Ch. 15 - Prob. 15PCh. 15 - Prob. 16PCh. 15 - Mercury is poured into a U-tube as shown in Figure...Ch. 15 - Prob. 18PCh. 15 - A backyard swimming pool with a circular base of...Ch. 15 - A tank with a flat bottom of area A and vertical...Ch. 15 - Prob. 21PCh. 15 - A Styrofoam slab has thickness h and density s....Ch. 15 - A table-tennis ball has a diameter of 3.80 cm and...Ch. 15 - The gravitational force exerted on a solid object...Ch. 15 - A 10.0-kg block of metal measuring 12.0 cm by 10.0...Ch. 15 - Prob. 26PCh. 15 - Prob. 27PCh. 15 - Prob. 28PCh. 15 - How many cubic meters of helium are required to...Ch. 15 - Prob. 30PCh. 15 - A plastic sphere floats in water with 50.0% of its...Ch. 15 - The weight of a rectangular block of low-density...Ch. 15 - Decades ago, it was thought that huge herbivorous...Ch. 15 - Prob. 34PCh. 15 - Prob. 35PCh. 15 - A light balloon is filled with 400 m3 of helium at...Ch. 15 - A horizontal pipe 10.0 cm in diameter has a smooth...Ch. 15 - Prob. 38PCh. 15 - A large storage tank with an open top is filled to...Ch. 15 - Review. Old Faithful Geyser in Yellowstone...Ch. 15 - (a) A water hose 2.00 cm in diameter is used to...Ch. 15 - Water flows through a fire hose of diameter 6.35...Ch. 15 - Prob. 43PCh. 15 - Prob. 44PCh. 15 - A village maintains a large tank with an open top,...Ch. 15 - Prob. 46PCh. 15 - Figure P15.47 shows a stream of water in steady...Ch. 15 - An airplane is cruising at altitude 10 km. The...Ch. 15 - The Bernoulli effect can have important...Ch. 15 - Prob. 50PCh. 15 - Prob. 51PCh. 15 - Prob. 52PCh. 15 - Prob. 53PCh. 15 - Prob. 54PCh. 15 - Prob. 55PCh. 15 - Prob. 56PCh. 15 - Prob. 57PCh. 15 - Prob. 58PCh. 15 - Review. A copper cylinder hangs at the bottom of a...Ch. 15 - Prob. 60PCh. 15 - An incompressible, nonviscous fluid is initially...Ch. 15 - In about 1657, Otto von Guericke, inventor of the...Ch. 15 - A 1.00-kg beaker containing 2.00 kg of oil...Ch. 15 - A beaker of mass mb containing oil of mass mo and...Ch. 15 - Prob. 65PCh. 15 - Prob. 66PCh. 15 - A U-tube open at both ends is partially filled...Ch. 15 - Prob. 68PCh. 15 - Prob. 69PCh. 15 - The spirit-in-glass thermometer, invented in...
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